The retrospective study is frequently the only practical means of investigating the association between certain exposure variables and a disease. With primary stimulation from the work of Cox (l972, Jour. Roy. Statist. Soc. B) statistical methods for prospective studies of such associations are now flexible and well developed. These methods, based on a proportional hazards regression model, permit the study of multiple time-dependent exposure variables on the relative risk of a disease, in the presence of confounding and effect modifying factors. In contrast, widely adopted statistical methods for the analysis of retrospective studies often involve reductions to simple dichotomous exposure variables and stratification to control confounding factors. Explicit account is usually not taken of the intermittent or cumulative nature of the exposure or of differing potential exposure times at disease incidence. Recent work by the applicants show that the prospective proportional hazards model can be used to induce a model for the retrospective study. Further, the parameters of interest, in the generality indicated above, can be estimated without further model assumption. This proposal is to further develop these new techniques and to make both empirical and theoretical comparisons with existing methods. One innovative aspect of this work will explore the feasibility of using cases that have incident disease late as controls for cases that have incident disease early. This may lead to the possibility of a retrospective study with no disease free individuals whatever. Several recent data sets already in our possession, as well as computer simulation, will be used to study formal statistical properties of the proposed methods.